Q.10 - The Practice of Statistics for AP

Question

Are TV commercials louder than their surrounding programs? To find out, researchers collected data on $50$ randomly selected commercials in a given week. With the television’s volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first $30$ seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is

(a) a one-proportion z test. 

(b) a one-proportion z interval. 

(c) a paired t test. 

Step-by-Step Solution

Answer

The correct answer is (c) a paired $t-$test.

Step 1: Given Information

The maximum loudness in the first $30$ seconds of regular programming that followed. 

Step 2: Explanation

The question of interest involves the population mean the difference between the commercial and the regular programming.

The normal distribution is used for the population proportion and the Student t-distribution is used for the population mean, thus we will need to use the Student t-distribution.

It is best to use a test because we wish to test if there is a difference or not, and thus the correct answer is (c) a paired $t$-test.